Pith Number

pith:RTP74IRR

pith:2026:RTP74IRRXJKHOSHIEB6RX7D7AP

not attested not anchored not stored refs resolved

On $p$-adic integral moduli schemes and local models for PEL type D

Ioannis Zachos, Jie Yang, Zhihao Zhao

Spin local models for even orthogonal similitude groups are flat, normal, and Cohen-Macaulay with reduced special fibers when the residue characteristic exceeds 2.

arxiv:2602.23813 v2 · 2026-02-27 · math.NT

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\pithnumber{RTP74IRRXJKHOSHIEB6RX7D7AP}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For an even orthogonal similitude group over a complete discretely valued field of residue characteristic p>2, and for arbitrary parahoric level, the associated spin local model is flat, normal, Cohen-Macaulay, with reduced special fiber.

C2weakest assumption

The assumption that the residue characteristic satisfies p>2, which is required to avoid characteristic-2 pathologies in the orthogonal group and its spin cover; the proof is stated only under this hypothesis.

C3one line summary

Proves flatness and related properties of spin local models for PEL type D and constructs flat orthogonal Rapoport-Zink spaces with parahoric level.

References

35 extracted · 35 resolved · 1 Pith anchors

[1] J. Ansch¨ utz, I. Gleason, J. Louren¸ co, T. Richarz,On thep-adic theory of local models, to appear inAnn. of Math. (2); preprint arXiv:2201.01234 (2022) 2022

[2] C.-L. Chai, P. Norman,Bad reduction of the Siegel moduli scheme of genus two withΓ 0(p)- level structure,Amer. J. Math.112(1990), no. 6, 1003–1071 1990

[3] P. Deligne, G. Pappas,Singularit´ es des espaces de modules de Hilbert, en les caract´ eristiques divisant le discriminant,Compositio Math.90(1994), 59–79 1994

[4] de Jong,The moduli spaces of principally polarized abelian varieties withΓ 0(p)-level struc- ture,J 1993

[5] de Jong,Smoothness, semi-stability and alterations,Publ 1996

Receipt and verification

First computed	2026-05-17T23:38:59.871695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cdffe2231ba547748e8207d1bfc7f03c4059a7448d9eb9d69f59ae1134a7b58

Aliases

arxiv: 2602.23813 · arxiv_version: 2602.23813v2 · doi: 10.48550/arxiv.2602.23813 · pith_short_12: RTP74IRRXJKH · pith_short_16: RTP74IRRXJKHOSHI · pith_short_8: RTP74IRR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RTP74IRRXJKHOSHIEB6RX7D7AP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8cdffe2231ba547748e8207d1bfc7f03c4059a7448d9eb9d69f59ae1134a7b58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e81fd36d78b618a6982a490edf13155e47df95fac39f84c76144c0f2a72d9abb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-02-27T08:53:23Z",
    "title_canon_sha256": "0ba6ab3e241fb8d964ecb629a6b288a1e70bd33875e6d357d3b0446e6b898174"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.23813",
    "kind": "arxiv",
    "version": 2
  }
}